Which of the following numbers is divisible by 11?

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Accepted Answer

**Solution:**

To check if a number is divisible by 11, use the rule:

1. Sum the digits in the odd positions (from right to left).
2. Sum the digits in the even positions.
3. Find the difference between these two sums.
4. If the difference is divisible by 11 (including 0), then the number is divisible by 11.

Let's verify each option:

- **Option 1: 5214341**
  - Odd position digits: 5 (1st) + 1 (3rd) + 3 (5th) + 1 (7th) = 5 + 1 + 3 + 1 = 10
  - Even position digits: 2 (2nd) + 4 (4th) + 4 (6th) = 2 + 4 + 4 = 10
  - Difference = 10 - 10 = 0, which is divisible by 11.
  - So, 5214341 is divisible by 11.

- **Option 2: 5648741**
  - Odd position digits: 5 + 4 + 7 + 1 = 17
  - Even position digits: 6 + 8 + 4 = 18
  - Difference = 17 - 18 = -1, not divisible by 11.

- **Option 3: 6598321**
  - Odd position digits: 6 + 9 + 3 + 1 = 19
  - Even position digits: 5 + 8 + 2 = 15
  - Difference = 19 - 15 = 4, not divisible by 11.

- **Option 4: 2378965**
  - Odd position digits: 2 + 7 + 9 + 5 = 23
  - Even position digits: 3 + 8 + 6 = 17
  - Difference = 23 - 17 = 6, not divisible by 11.

**Answer:** 5214341 is divisible by 11.

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